A transmission link which is used for asynchronous transfer mode (ATM) transmission is divided, with regard to time, into a plurality of successive cells. When such a link is used for transmitting data packets on several channels, each channel is identified with the aid of an address field in each cell. If packets with different intensities are set on different channels, an individual bandwidth is obtained for each channel. The sum of the bandwidths of all channels must therefore be less than the maximum bandwidth of the link. In order that one channel not interfere with remaining channels by utilizing a bandwidth which is too great, it is desirable for the channels to be monitored so that packets with higher intensity than what was initially determined for the respective channel are not sent on any channel.